Coursework Requirements for the AIM Ph.D.
Students in the AIM Ph.D. program take both mathematics courses and courses from other departments. In addition, to facilitate the choice of a partner discipline and to illustrate the breadth of interdisciplinary research, the program requires students to enroll in the AIM Student Seminar (Math 501) for the first three semesters.
Basic Requirements
The AIM Ph.D. degree requires a minimum of 11 regular courses (3 credits each) and 3 credits of
the AIM Student Seminar (Math 501). Remaining coursework should be composed of Candidate Research (Math 995) or other approved graduate courses. The AIM coursework requirements exceed those of the regular mathematics
Ph.D., but the needs of interdisciplinary research mandate a more extensive
type of graduate training. The 11 regular courses should be composed of the following:
 a total of at least seven mathematics courses, which must include at least four AIM core courses (see below) and at least an additional two math courses at or above the 600 level.
 at least four graduate level courses from the chosen partner field, or another field outside of mathematics.
All courses must be at the graduate level (400 level and above), and
with the exception of Math 501 must be graded courses completed with a grade of at least B, with an overall average of B+.
The AIM Program Director will
supervise coursework selection in the first two years. Coursework in
subsequent years is normally supervised by the mathematics and partner discipline coadvisors.
AIM Core Courses
The following courses are fundamental to many areas of applied mathematics and related application areas. These courses provide the basic mathematical framework on which the AIM graduate experience is built.
 Math 525. Probability Theory
 Math 526. Stochastic Processes
 Math 555. Complex Variables
 Math 556. Methods of Applied Math I: Applied Functional Analysis
 Math 557. Methods of Applied Math II: Asymptotic Analysis
 Math 558. Applied Nonlinear Dynamics
 Math 565. Combinatorics and Graph Theory
 Math 566. Combinatorial Theory
 Math 571. Numerical Methods for Scientific Computing I: Numerical Linear Algebra
 Math 572. Numerical Methods for Scientific Computing II : Numerical Methods for Differential Equations
 Math 656. Introduction to Partial Differential Equations
 Math 657. Nonlinear Partial Differential Equations
Well prepared students may, with permission, substitute alternate mathematics courses
for some AIM core courses.
The AIM Student Seminar Course  Math 501
The AIM Student Seminar course is a threesemester sequence taken by all AIM Ph.D. students (AIM M.S. students will join the course for the first two semesters of study). It is specifically designed to assist with many of the unique challenges confronting AIM graduate students. For Ph.D. students, one of these challenges is the choice of a dissertation committee that includes two different coadvisors, one from mathematics and one from another partner discipline. Another challenge common to the interests of both M.S. and Ph.D. students is the development of a sound understanding of the way that mathematics plays a role in diverse application areas.
Math 501 is a course only for AIM graduate students. It is coordinated with the departmental Applied and Interdisciplinary Mathematics Research Seminar, and students are required to participate in the research seminar on a weekly basis as a course requirement. Students will therefore meet once each week during the regular course time and again during the time of the research seminar. Currently these two meetings are scheduled for 121 PM and 34 PM respectively on Fridays. Attendance of the AIM research seminar as part of Math 501 is vital to sound interdisciplinary training. In this way, students
will be exposed to a wide range of research topics.
The specific content of the Math 501 course as delivered during the regular course meetings is highly variable, but the purpose of the course is clear: to address specific issues related to the process of successfully completing a graduate degree
in the AIM program and becoming an active member of the research community. The weekly
meetings of the class are generally partitioned among three types of sessions:
 “Focus on. . ." presentations. These are short presentations on various subjects pertinent to
the pursuit of an AIM degree as well as other aspects of professional development. In prior semesters some of the presentations have been:
 Focus on . . . how to find your advisor and coadvisor
 Focus on . . . how to use the library at the University of Michigan
 Focus on . . . applying for summer research programs
 Focus on . . . using LATEX for scholarly writing
 AIM Faculty Portraits. These are short presentations by faculty members from mathematics and other departments, providing a direct channel for students to discover what research is
being done in various application areas, and to see what kind of preparation is required for participating in
such research. Any faculty member giving an AIM Faculty Portrait is a potential thesis coadvisor for AIM Ph.D.
students.
 AIM Research Seminar “Warmup talks". These are presentations by particularly dynamic speakers slated to speak in the AIM
Research Seminar (or surrogates thereof) as a way to provide background material with the goal
of making the AIM Research Seminar lecture more valuable for the AIM students. The warmup talks will (i) present the background to the research to be discussed
at a more advanced level in the subsequent Research Seminar talk, (ii) put the work in context
and discuss the importance of the results, and (iii) generally provide an introduction to
topic of the Research Seminar. This enables students to derive greater benefit from the AIM Research Seminar series and to gain meaningful exposure to a broad range of
problems.
Suggested Mathematics and Partner Discipline Courses
Here we list some courses that might be appropriate for AIM graduate students. Reading courses may also be arranged between students and willing faculty from mathematics or other departments. These can provide opportunities for personalized instruction going beyond what is available in regular courses, and can count for course credit.
Example Course Tracks
Here are some sample course tracks in various application areas. The color scheme for the courses is as follows:
 Red text: AIM Student Seminar course
 Blue text: AIM Core courses (or equivalents)
 Magenta text: Partner discipline courses
A Student Preparing for Research in Electrical Engineering (Image Processing):

Fall Semester 
Winter Semester 
Year 1 
MATH 501 (AIM Student Seminar)
MATH 556 (Methods of Applied Mathematics I)
MATH 561 (Linear Programming I)
MATH 571 Numerical Scientific Computing I) 
MATH 501 (AIM Student Seminar)
MATH 525 (Probability)
MATH 557 (Methods of Applied Mathematics II)
MATH 563 (Advanced Mathematical Biology) 
Year 2 
MATH 501 (AIM Student Seminar)
IOE 612 (Network Flows)
MATH 558 (Ordinary Differential Equations)
MATH 651 (Topics in Applied Mathematics I) 
EECS 586 (Algorithms)
IOE 611 (Nonlinear Programming)
MATH 526 (Discrete Stochastic Processes) 
Year 3 
EECS 587 (Parallel Computing)
MATH 656 (Introduction to Partial Differential Equations) 
PHYSICS 406 (Statistical and Thermal Physics) 
A Student Preparing for Research in Mathematical Biology (Cancer Modeling):

Fall Semester 
Winter Semester 
Year 1 
MATH 501 (AIM Student Seminar)
MATH 463 (Mathematical Modeling in Biology)
MATH 525 (Probability)
MATH 555 (Complex Variables) 
MATH 501 (AIM Student Seminar)
MATH 513 (Introduction to Linear Algebra)
MATH 558 (Ordinary Differential Equations)
MATH 563 (Advanced Mathematical Biology) 
Year 2 
MATH 501 (AIM Student Seminar)
EPID 511 (Introduction to Public Health Genetics)
MATH 556 (Methods of Applied Mathematics I)
MICROBIOL 553 (Cancer Biology) 
MATH 567 (Introduction to Coding Theory)
MATH 572 (Numerical Scientific Computing II)

Year 3 
EHS 513 (Pathology and the Basis of Disease)
MATH 656 (Introduction to Partial Differential Equations)
MATH 671 (Numerical Methods I) 
MICROBIOL 440 (Immunology) 
A Student Preparing for Research in Computer Science (Compressive Sampling):

Fall Semester 
Winter Semester 
Year 1 
MATH 501 (AIM Student Seminar)
MATH 525 (Probability)
MATH 555 (Complex Variables)
MATH 591 (General and Differential Topology)

MATH 501 (AIM Student Seminar)
MATH 526 (Discrete Stochastic Processes)
MATH 566 (Combinatorial Theory)
MATH 567 (Introduction to Coding Theory) 
Year 2 
MATH 501 (AIM Student Seminar)
ECON 617 (Game Theory)
EECS 574 (Computational Complexity)
MATH 556 (Methods of Applied Mathematics I) 
EECS 684 (Current Topics in Databases)
MATH 597 (Real Analysis and Measure Theory)
STATS 701 (Topics in Appl. Statistics II  Large Data Sets) 
Year 3 
MATH 547 (Probabilistic Modeling in Bioinformatics)
MATH 654 (Introduction to Fluid Mechanics) 
MATH 650 (Fourier Analysis)
STATS 711 (Topics in Theoretical Statistics II)

A Student Preparing for Research in Fluid Mechanics (Geophysical Fluid Flow):

Fall Semester 
Winter Semester 
Year 1 
MATH 501 (AIM Student Seminar)
MATH 525 (Probability)
MATH 602 (Real Analysis II / Functional Analysis)
PHYSICS 401 (Mechanics)

MATH 501 (AIM Student Seminar)
MATH 557 (Methods of Applied Mathematics II)
MATH 572 (Numerical Scientific Computing II) MATH 710 (Modern Analysis II) 
Year 2 
MATH 501 (AIM Student Seminar)
AOSS 420 (Environmental and Ocean Dynamics)
MATH 558 (Ordinary Differential Equations)
MATH 654 (Introduction to Fluid Mechanics)
MATH 656 (Introduction to Partial Differential Equations) 
AOSS 605 (Current Topics / Physical Climate)
MATH 526 (Discrete Stochastic Processes)
PHYSICS 406 (Statistical and Thermal Physics) 
Year 3 
AOSS 605 (Current Topics / WaveMean Flow Interaction)
MATH 756 (Advanced Partial Differential Equations) 
AOSS 422 (Boundary Layer Methods)
GEOSCI 500 (Computer Programming for Geoscience)

A Student Preparing for Research in Mathematical Finance:
Note: this example illustrates the possibility of an exceptionally wellprepared student substituting a higherlevel course (MATH 626) for a corresponding AIM Core course (in this case, MATH 526).

Fall Semester 
Winter Semester 
Year 1 
MATH 501 (AIM Student Seminar)
MATH 525 (Probability)
MATH 565 (Combinatorics and Graph Theory)
STATS 620 (Applied Probability and Stochastic Modeling) 
MATH 501 (AIM Student Seminar)
MATH 572 (Numerical Scientific Computing II)
MATH 650 (Fourier Analysis)
STATS 625 (Statistics of Random Processes) 
Year 2 
MATH 501 (AIM Student Seminar)
FIN 580 (Options, Futures, and Corporate Decision Making)
MATH 656 (Introduction to Partial Differential Equations) 
EECS 498 (Special Topics / C++ Programming)
IOE 552 (Financial Engineering I)
MATH 625 (Probability and Random Processes I) 
Year 3 
ECON 407 (Finance Econometrics)
IOE 553 (Financial Engineering II)
STATS 610 (Statistical Inference) 
MATH 623 (Computational Finance)
MATH 626 (Probability and Random Processes II) 
